Entanglement spectrum ordering and flavor polarization in the two-flavor Schwinger model at vacuum angle θ = π

On finite open staggered chains of the two-flavor Schwinger model at vacuum angle θ = π, we resolve the joint Schmidt distribution p(Q_A,F_A), labeled by subsystem gauge charge Q_A and flavor imbalance F_A. Defining the combined weight W_F^(q) = p_(q,+1) + p_(q,-1) and conditional polarization P_F^(q) = [p_(q,+1) - p_(q,-1)]/W_F^(q), we find that changing the staggered cut reverses the nonneutral pair weight hierarchy: W_F^(-1) > W_F^(+1) at unit cell boundaries, but W_F^(+1) > W_F^(-1) at intracell cuts. The signed polarization further shows that positive charge fluctuations at intracell cuts can favor the heavier flavor despite its larger bare excitation cost. At fixed masses, hopping, and geometry, increasing the background field suppresses p_(+1,-1) more strongly than p_(+1,+1), driving P_F^(+1) through zero and overturning the initial light flavor advantage. Matched Hamiltonian controls show that the external source alone can produce P_F^(+1) > 0 at intermediate θ, while electric self energies sustain an appreciable W_F^(+1) with P_F^(+1) > 0 at θ = π; direct interflavor coupling weakens this preference and delays the crossing. Thus symmetry resolution distinguishes gauge sector ordering from flavor composition and reveals why a lower bare excitation cost need not determine the flavor composition of a charged vacuum fluctuation. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.